Computation of Force Closure Computation of Force Closure Grasps from Finite Contact Grasps from Finite Contact

Point SetPoint SetNattee NiparnanNattee Niparnan

Advisor: Dr. Attawith SudsangAdvisor: Dr. Attawith Sudsang

General OutlineGeneral Outline

The story so far: The story so far: robotic graspingrobotic grasping What lies behind us: What lies behind us: literature reviewliterature review Where shall we go: Where shall we go: the problemthe problem Who walk along the same road: Who walk along the same road: related workrelated work Problem DetailProblem Detail

Grasping BasicGrasping Basic

How do we reach the goal: How do we reach the goal: attack pointattack point Boring stuffs

work plan, objective, scopes, benefit

Robotic GraspingRobotic Grasping

To hold an object firmlyTo hold an object firmlyPrevent motion of an objectPrevent motion of an object

State of the ArtState of the Art

Ultimate Goal of GraspingUltimate Goal of Grasping

Sense the objectSense the objectCalculate grasping positionCalculate grasping position Initiate a graspInitiate a grasp

Grasping ComponentsGrasping Components

Task Model

Algorithm

Hand Model

Purpose of grasp

• Power grasp

• Dexterous grasp

• Tool-specific grasp

Physical of hands

• Power

• Degree of Freedom

• Hand property

Grasp Planning

• Where to grasp

Objective Function

Graspingconstraints

Grasp PlanningAlgorithm

Example: Grasping a HammerExample: Grasping a Hammer

Task: Moving a HammerTask: Moving a HammerMaximize stabilityMaximize stability

Task: Using a HammerTask: Using a HammerMaximize head speedMaximize head speed

Hand: Parallel Jaw GripperHand: Parallel Jaw GripperHand: 4-fingered HandHand: 4-fingered Hand

Grasp Planning AlgorithmGrasp Planning Algorithm

AlgorithmObject to be grasped

GraspingConfiguration

InputOutput

What comes before usWhat comes before us

80’s 200690’s

Grasping Definition

•Hanafusa Asada ’77, ’79

•Ohwovoriore ‘80

•Salisbury ’82

•Asada By ’85

•Nguyen ’88, ’89

Existence of Grasps

•Lakshminarayara ’78

•Mishra et al. ’87

•Markenscoff et al. ’89

200019001800Reuleaux

Grasping Quality

•Li Sastry ’88

•Kirkpatric et al. ’90

•Ferarri Canny ’92

•Trinkle ’92

Grasp Planning

•Ponce et al. ’95

•Lui ’99 – ’05

•Li et al ’03

•Zhu Wang ’03

Sumov

Hand ModelHand Model

Utah/MIT Dextrous Hand

Barrette Hand DLR Hand II

Robonaut Hand

Task ModelTask Model

Grasping Objective FunctionGrasping Objective Function

ToleranceMinimize

effect ToleranceMinimize

effect

Stability Accuracy

ObjectiveFunction

•Kirkpatric et al

•Ferrari Canny

•Ponce et al

•Lui et al

•Ponce et al.

•Nguyen

•Ding et al

Conventional GraspingConventional Grasping

ObjectiveFunction Hand ModelHand Model

Hand Model

ObjectiveFunctionTask Model

Customizedalgorithm

IssuesIssues

No generally good grasp!!!No generally good grasp!!!No general task modelNo general task modelNo general hand modelNo general hand modelDifferent measurement and constraintsDifferent measurement and constraints

Object modelingObject modelingModeling accuracyModeling accuracy

Object ModelingObject Modeling

Modeling accuracyModeling accuracy PolygonPolygon

LinearLinear Low accuracyLow accuracy

CurveCurve High cost of curve fittingHigh cost of curve fitting NonlinearNonlinear High AccuracyHigh Accuracy

Contact pointsContact points High number of contact pointsHigh number of contact points Almost the same accuracy of curveAlmost the same accuracy of curve PracticalPractical

Polygon

CurveContact

Point

Where shall we goWhere shall we go

New grasp planning frameworkNew grasp planning framework

Hand ModelTask Model

GeneralizedAlgorithm Take no a priori

knowledge

Use Contact Points(Model-less)

Where shall we goWhere shall we go

Instead of finding one best graspInstead of finding one best graspJust find “firm” graspsJust find “firm” grasps

Find lots of graspsFind lots of graspsUse no a priori knowledge of Task/HandUse no a priori knowledge of Task/HandLet task model and hand model choose Let task model and hand model choose

appropriate graspappropriate graspUsing contact pointsUsing contact points

Model-less inputModel-less inputa large number of inputa large number of input

Is It Hard?Is It Hard?

Consider one single “Consider one single “firm graspfirm grasp” problem in ” problem in Polygonal modelPolygonal model Computational intensiveComputational intensive Linear Programming / Ray Shooting / Point InclusionLinear Programming / Ray Shooting / Point Inclusion

Multiple grasping solution?Multiple grasping solution? Almost unobtainable until recentlyAlmost unobtainable until recently

With contact point model?With contact point model? Polygon Polygon around around 10-2010-20 faces faces Contact Point Contact Point around around 10001000 contact points contact points Much more computational extensiveMuch more computational extensive

ChallengeChallenge

SPEED!!!SPEED!!!

Usage of the ResultUsage of the Result

Given Task/HandGiven Task/Handenumerate solution to find the best oneenumerate solution to find the best oneO(n)O(n)

Result is associated to the objectResult is associated to the objectNormal use usually involve multiple stepNormal use usually involve multiple stepRegraspRegrasp

Problem Statement: First DraftProblem Statement: First Draft

Given a set of contact pointsGiven a set of contact pointsFindFind

As many good grasps as possibleAs many good grasps as possible In a short timeIn a short time

Naïve ApproachNaïve Approach

one single “one single “firm firm graspgrasp” problem” problem

Still is an active topicStill is an active topic Lui ’99 – ’05 Li et al ’03 Zhu Wang ’03 Borst et al ’03 Zhu et al ’04

Naïve ApproachNaïve Approach

Finding all solutionsFinding all solutions Combinatorial Combinatorial ProblemProblem 1000 points1000 points 4 fingers4 fingers

Must checkMust check

O(NO(N44)) Search spaceSearch space

1000

4

Who walk along the same roadWho walk along the same road

Contact point inputContact point input Wallack Canny ‘Wallack Canny ‘9494 Brost Goldberg ‘Brost Goldberg ‘9696 Wang ‘Wang ‘0000

Multiple solutionsMultiple solutions van der Stappen ‘van der Stappen ‘0404

Multiple solutions & Contact point InputMultiple solutions & Contact point Input None...None...

Problem DetailProblem Detail

Grasping BasicGrasping Basic

Force ClosureForce ClosureFormal definition of firm graspFormal definition of firm grasp ““Hand can influence the object such that any Hand can influence the object such that any

external disturbance can be nullified”external disturbance can be nullified”

Influence of a handInfluence of a hand

via contact points between a hand and an via contact points between a hand and an objectobject

Described by Described by Contact positions ( r )Contact positions ( r )Contact directions ( n )Contact directions ( n )

Influence of a Contact PointInfluence of a Contact Point

Force (contact direction)Force (contact direction)Force vector Force vector ( f )( f )

Torque (contact position & direction)Torque (contact position & direction)Torque vector Torque vector ( r x f )( r x f )

WrenchWrench

To combine force and torque into one To combine force and torque into one componentcomponent Easier to describe Easier to describe

Wrench = force vector concatenates with torque Wrench = force vector concatenates with torque vectorvector

w = ( f, r x f )w = ( f, r x f ) Model a contact point by a wrenchModel a contact point by a wrench

Space Space DimensionDimension

ForceForceDimensionDimension

TorqueTorqueDimensionDimension

Wrench Wrench DimensionDimension

2D2D 2D2D 1D1D 3D3D

3D3D 3D3D 3D3D 6D6D

Wrench ExampleWrench Example

Force Closure in terms of Force Closure in terms of WrenchesWrenches

External disturbance can also be written External disturbance can also be written as a wrenchas a wrench

Contact points can exertContact points can exertTheir respective wrenchesTheir respective wrenches

Also Also positive combinationspositive combinations of the wrenches of the wrenches

Force Closure = Force Closure = any wrenchany wrench can be can be expressed by a positive combination of expressed by a positive combination of contact point wrenchescontact point wrenches

GraspingHand

Contact Points

Forces &Torques

Wrenches

Problem TransformationProblem Transformation

EquivalenceEquivalenceWrenches achieve Wrenches achieve force closureforce closureWrenches Wrenches positively span positively span RR66 (or R (or R33))A A Convex hullConvex hull of wrenches of wrenches contains the origincontains the origin

GraspingHand

Contact Points

Forces &Torques

Wrenches

ForceClosure?

Positively Spanning

?

The origin inside CH?

Positively SpanningPositively Spanning

any vector can be expressed by any vector can be expressed by a positive a positive combinationcombination of given vectors of given vectors

Point in Convex HullPoint in Convex Hull

The origin is The origin is strictly insidestrictly inside the convex hull the convex hull of contact point vectorsof contact point vectors In the In the interiorinterior of the convex hull of the convex hull

Contact Model (Friction)Contact Model (Friction)

With frictionWith frictionOne contact point is associated with One contact point is associated with many many

wrencheswrenches

Check PointCheck Point

Grasping problem isGrasping problem isA mathematical problemA mathematical problemA computational geometry problemA computational geometry problem

Emphasize on deriving of an efficient Emphasize on deriving of an efficient algorithm for reporting algorithm for reporting several solutionsseveral solutions from from contact point inputcontact point input

Problem ConfigurationProblem Configuration

Object Model

Role Contact Model

Finger

Contact point

Curved object

Polygon

Optimizer

ClassifierFrictionless

Frictional

3 fingers (2D)

4 fingers (2D,3D)

2 fingers

n fingers

7 fingers (3D)

The Problem: RevisitedThe Problem: Revisited

Input: A set of contact pointsInput: A set of contact pointsOutput: A set of grasping solutionsOutput: A set of grasping solutionsCombinatorial problemCombinatorial problem

Algorithm

ContactPoints

aswrenches Sol

SolSol

SolSol

Sol

Sol

Sol Sol

Sol

2D Frictional(3 fingers)

2D Frictionless(4 fingers)

3D Frictional(4 fingers)

3D Frictionless(7 fingers)

How do we reach the goalHow do we reach the goal

Exploit multiple solution nature of the Exploit multiple solution nature of the problemproblemTry to use pre-computationTry to use pre-computation

Sorting, searching, suitable data structure, etc.Sorting, searching, suitable data structure, etc.

Problem reformulationProblem reformulationReduce dimension of wrench spaceReduce dimension of wrench space

Work PlanWork Plan Study the works in the related fieldsStudy the works in the related fields Preliminary works on a heuristic algorithm Preliminary works on a heuristic algorithm Study a reformulation of the problemStudy a reformulation of the problem In-depth study of grasp planning algorithmsIn-depth study of grasp planning algorithms Perform extensive comparison of various Perform extensive comparison of various

grasping conditiongrasping condition Develop algorithmsDevelop algorithms ComparisonComparison Publish a journal articlePublish a journal article Prepare and engage in a thesis defensePrepare and engage in a thesis defense

Recent WorksRecent Works Fast Computation of 4-Fingered Force-Closure Grasps from Surface PointsFast Computation of 4-Fingered Force-Closure Grasps from Surface Points. .

Proc. of the IEEE/RSJ International Conf. on Intelligent Robots and Proc. of the IEEE/RSJ International Conf. on Intelligent Robots and Systems, pp 3692-3697, 2004. Systems, pp 3692-3697, 2004.

Regrasp Planning of Four-Fingered Hand for Parallel Grasp of a Polygonal Regrasp Planning of Four-Fingered Hand for Parallel Grasp of a Polygonal Object.Object. Proc. of the IEEE International Conf. on Robotics and Automation, Proc. of the IEEE International Conf. on Robotics and Automation, pp 791-796, 2005. pp 791-796, 2005.

A Heuristic Approach for Computing Frictionless Force-Closure Grasps of A Heuristic Approach for Computing Frictionless Force-Closure Grasps of 2D Objects2D Objects from Contact Point Set. Proc. of the IEEE International from Contact Point Set. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Conference on Robotics, Automation and Mechatronics, 2006

Planning Optimal Force-Closure Grasps for Curved Objects by Genetic Planning Optimal Force-Closure Grasps for Curved Objects by Genetic Algorithm.Algorithm. Proc. of the IEEE International Conference on Robotics, Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Automation and Mechatronics, 2006

4-Fingered Force-Closure Grasps from Surface Points using Genetic 4-Fingered Force-Closure Grasps from Surface Points using Genetic Algorithm .Algorithm . Proc. of the IEEE International Conference on Robotics, Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Automation and Mechatronics, 2006

ObjectiveObjective

To develop efficient algorithms that report To develop efficient algorithms that report several force closure grasps from a set of several force closure grasps from a set of finite contact pointsfinite contact points

Scope of the ResearchScope of the Research

Considers force closure grasping in both Considers force closure grasping in both 2D and 3D in friction and frictionless case2D and 3D in friction and frictionless case

Derived algorithms must work faster than Derived algorithms must work faster than an enumerative approach that uses the an enumerative approach that uses the fastest computationfastest computation

Performance measurement can be either Performance measurement can be either an actual running time (in case of a an actual running time (in case of a heuristic algorithm) or a complexity heuristic algorithm) or a complexity analysis (in case of a complete algorithm)analysis (in case of a complete algorithm)

Scope of the ResearchScope of the Research

2D Frictional(3 fingers)

2D Frictionless(4 fingers)

3D Frictional(4 fingers)

3D Frictionless(7 fingers)

Compare with the best known “single solution” algorithm

Evidence of superiority•Proof of complexity analysis•Running Time Comparison

Evidence of superiority•Proof of complexity analysis•Running Time Comparison

Evidence of superiority•Proof of complexity analysis•Running Time Comparison

Evidence of superiority•Proof of complexity analysis•Running Time Comparison

Expected ContributionExpected Contribution

Having algorithms that report several force Having algorithms that report several force closure grasps from a set of discrete closure grasps from a set of discrete contact points.contact points.

Thank YouThank You

Comments are heartily welcomedComments are heartily welcomed

Coulomb FrictionCoulomb Friction

fn

ft = ufN

a = tan-1(u)

DLR HandDLR Hand

Sensor per each fingerSensor per each finger 3 joint position sensors:3 joint position sensors: 3 joint torque sensors:3 joint torque sensors: 3 motor position/speed 3 motor position/speed

sensors: sensors: 1 six-dimensional 1 six-dimensional fingerfinger tiptip

force torque force torque sensorsensor:: 3 motor temperature 3 motor temperature

sensors: sensors: 3 sensors for temperature 3 sensors for temperature

compensation: integrated compensation: integrated sensorssensors